Camera Shake in 3d video games
This can be accomplished with the "slow parent" settings. They are found under Properties > Object > Relations Extras. Open them up under the camera and turn the offset up to, say, 9.00. This will give a lot of drag between your camera following the player; When the player moves, the camera follows loosely, just like you wanted. If you want a longer time between parent movement ad the child movement, increase the offset, less time, decrease the offset.